Timoshenko beam-column with generalized end conditions on elastic foundation: Dynamic-stiffness matrix and load vector

Arboleda-Monsalve, Luis G.; Zapata-Medina, David G.; Aristizábal-Ochoa, J. Darío

doi:10.1016/j.jsv.2007.08.014

Cited by 56 publications

(16 citation statements)

References 19 publications

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“…The analysis of a beam resting on two-parametrical elastic foundation has been conducted by many authors [24][25][26][27][28][29][30][31][32][33]. A majority of them employed a fi nite element formulation to perform analyses.…”

Section: Introductionmentioning

confidence: 99%

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Vibrations And Stability Of Bernoulli-Euler And Timoshenko Beams On Two-Parameter Elastic Foundation

Obara

2014

Archives of Civil Engineering

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The vibration and stability analysis of uniform beams supported on two-parameter elastic foundation are performed. The second foundation parameter is a function of the total rotation of the beam. The effects of axial force, foundation stiffness parameters, transverse shear deformation and rotatory inertia are incorporated into the accurate vibration analysis. The work shows very important question of relationships between the parameters describing the beam vibration, the compressive force and the foundation parameters. For the free supported beam, the exact formulas for the natural vibration frequencies, the critical forces and the formula defi ning the relationship between the vibration frequency and the compressive forces are derived. For other conditions of the beam support conditional equations were received. These equations determine the dependence of the frequency of vibration of the compressive force for the assumed parameters of elastic foundation and the slenderness of the beam.

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Section: Introductionmentioning

confidence: 99%

“…The dynamic stiffness matrix and the load vector of the Timoshenko beam-column resting on the two-parameter elastic foundation with generalized end condition were presented in Ref. [28]. The static, dynamic and stability behavior of framed structures made of beam-columns were analyzed in that paper.…”

Section: Introductionmentioning

confidence: 99%

Vibrations And Stability Of Bernoulli-Euler And Timoshenko Beams On Two-Parameter Elastic Foundation

Obara

2014

Archives of Civil Engineering

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“…The solution to ordinary differential equation (18) can be expressed by φ n (x) = C 1n e iβ 1n x + C 2n e iβ 2n x + C 3n e iβ 3n x + C 4n e iβ 4n x .…”

Section: The Multi-scale Analysismentioning

confidence: 99%

“…Challamel [17] compared the Timoshenko model with shear model for stationary beams without axial translations. Arboleda-Monsalve, Zapata-Medina, and AristizabalOchoa [18] presented the dynamic-stiffness matrix and load vector of a Timoshenko beam-column resting on a two-parameter elastic foundation with generalized end conditions. Ghayesh and Khadem [19] investigated free nonlinear transverse vibration of an axially moving beam.…”

Section: Introductionmentioning

confidence: 99%

Parametric resonance of axially moving Timoshenko beams with time-dependent speed

Tang¹,

Chen

Yang

2009

Nonlinear Dyn

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In this paper, parametric resonance of axially moving beams with time-dependent speed is analyzed, based on the Timoshenko model. The Hamilton principle is employed to obtain the governing equation, which is a nonlinear partial-differential equation due to the geometric nonlinearity caused by the finite stretch of the beam. The method of multiple scales is applied to predict the steady-state response. The expression of the amplitude of the steady-state response is derived from the solvability condition of eliminating secular terms. The stability of straight equilibrium and nontrivial steady-state response are analyzed by using the Lyapunov linearized stability theory. Some numerical examples are presented to demonstrate the effects of speed pulsation and the nonlinearity in the first two principal parametric resonances.

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“…On the other hand, the effects of shear deformation and rotary inertia have been taken into account in linear dynamic analysis of beams [16,17], in linearized dynamic or stability analysis [18][19][20][21][22] ignoring the squares of the derivatives of the deflections in the normal strain component and the axial differential equation of equilibrium and in free vibrations of beams with special boundary conditions performing a nonlinear dynamic analysis. More specifically for this latter case, Rao et al [23], employing the finite element method and polynomial expressions for the displacement components, presented the large amplitude free vibrations of slender beams.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamic analysis of Timoshenko beams by BEM. Part I: Theory and numerical implementation

Sapountzakis

Dourakopoulos

2009

Nonlinear Dyn

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In this two-part contribution, a boundary element method is developed for the nonlinear dynamic analysis of beams of arbitrary doubly symmetric simply or multiply connected constant cross section, undergoing moderate large displacements and small deformations under general boundary conditions, taking into account the effects of shear deformation and rotary inertia. Part I is devoted to the theoretical developments and their numerical implementation and Part II discusses analytical and numerical results obtained from both analytical or numerical research efforts from the literature and the proposed method. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions as well as to axial loading. To account for shear deformations, the concept of shear deformation coefficients is used. Five boundary value problems are formulated with respect to the transverse displacements, to the axial displacement and to two stress functions and solved using the Analog Equation Method, a BEM based method. Application of the boundary element technique yields a nonlinear coupled system of equations of motion. The solution of this system is accomplished iteratively by employing the average acceleration method in combination with the modified Newton-Raphson method. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. The proposed model takes into account the coupling effects of bending and shear deformations along the member, as well as the shear forces along the span induced by the applied axial loading.

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Timoshenko beam-column with generalized end conditions on elastic foundation: Dynamic-stiffness matrix and load vector

Cited by 56 publications

References 19 publications

Vibrations And Stability Of Bernoulli-Euler And Timoshenko Beams On Two-Parameter Elastic Foundation

Vibrations And Stability Of Bernoulli-Euler And Timoshenko Beams On Two-Parameter Elastic Foundation

Parametric resonance of axially moving Timoshenko beams with time-dependent speed

Nonlinear dynamic analysis of Timoshenko beams by BEM. Part I: Theory and numerical implementation

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